New Evidence on Causal Relationship between Approximate Number System (ANS) Acuity and Arithmetic Ability in Elementary-School Students: A Longitudinal Cross-Lagged Analysis.

He Y, Zhou X, Shi D, Song H, Zhang H, Shi J - Front Psychol (2016)

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Figure 3: The fitted optimal cross-lagged model (M2) with standardized path coefficients. The numbers attached to the arrows were standardized path coefficients, with sig errors in the brackets.
Mentions: Table 3 summarizes the fit indices of the four competing cross-lagged models, i.e., M1 (with no cross-lagged effect), M2 (with cross-lagged effect from ANS acuity to arithmetic ability), M3 (with cross-lagged effect from arithmetic ability to ANS acuity), and M4 (with reciprocal cross-lagged effects). The four indices suggest that M1 demonstrates a good fit to the data (χ2 (8) = 23.456, TLI = 0.904, CFI = 0.945, RMSEA = 0.098). Furthermore, by adding the cross-lagged path from ANS acuity to arithmetic ability, M2 shows significant improvement of fit to the data compared to M1 (Δχ2 (1) = 9.624, p < 0.001); in contrast, M3 shows no significant improvement when adding the cross-lagged paths from arithmetic ability to ANS acuity (Δχ2 (1) = 0.766, p = 0.381). Furthermore, a close comparison between M4 and M2 shows that adding the cross-lagged paths from arithmetic ability to ANS acuity does not improve the fit of M2 to the data (Δχ2 (1) = 0.324, p = 0.569). Therefore, the cross-lagged effect from arithmetic ability to ANS acuity was not supported. M2 was selected as the best-fitted model, and the standardized regression coefficients of M2 are shown in Figure 3

Bottom Line: Approximate number system (ANS) acuity and mathematical ability have been found to be closely associated in recent studies.The results show that ANS acuity influences later arithmetic ability while the reverse causal direction was not supported.Our finding adds a strong evidence to the causal association between ANS acuity and mathematical ability, and also has important implications for educational intervention designed to train ANS acuity and thereby promote mathematical ability.

View Article: PubMed Central - PubMed

Affiliation: Key Laboratory of Behavioral Science, Institute of Psychology, Chinese Academy of Sciences Beijing, China.

ABSTRACT
Approximate number system (ANS) acuity and mathematical ability have been found to be closely associated in recent studies. However, whether and how these two measures are causally related still remain less addressed. There are two hypotheses about the possible causal relationship: ANS acuity influences mathematical performances, or access to math education sharpens ANS acuity. Evidences in support of both hypotheses have been reported, but these two hypotheses have never been tested simultaneously. Therefore, questions still remain whether only one-direction or reciprocal causal relationships existed in the association. In this work, we provided a new evidence on the causal relationship between ANS acuity and arithmetic ability. ANS acuity and mathematical ability of elementary-school students were measured sequentially at three time points within one year, and all possible causal directions were evaluated simultaneously using cross-lagged regression analysis. The results show that ANS acuity influences later arithmetic ability while the reverse causal direction was not supported. Our finding adds a strong evidence to the causal association between ANS acuity and mathematical ability, and also has important implications for educational intervention designed to train ANS acuity and thereby promote mathematical ability.

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